Getting up to speed in turbulence simulations

Turbulent flow spans a broad range of time and length scales, from large-scale sloshing down to the tiniest eddies. Bridging those scales in a numerical simulation is notoriously difficult, and even a modest system requires extensive amounts of computing time. Moreover, before most simulations start producing useful data, they must first be “spun up,” taken through sufficient computational cycles to reach statistical equilibrium. Some simulations can take a shortcut: starting with the final conditions from previous runs. But others, lacking an appropriate data set for initialization, can’t escape the extensive extra computational burden. Kurt Nelson and Oliver Fringer of Stanford University now report a method that can significantly reduce spin-up time. They consider the case of open-channel flow, in which fluid of a given depth is constrained by walls on opposite sides and below; the approach, though, is broadly generalizable. Simulated flows are typically driven by an applied pressure gradient, but the researchers find that such an approach overshoots a steady-state velocity, prolonging spin-up. So they instead enforce a constant volume-averaged downstream velocity. The required driving force, it turns out, exactly balances the frictional drag along the channel bottom at each iteration, and the overshoot is avoided. Although the simulated flow has the correct average velocity, the transition to turbulence does still take computer time. The figure illustrates the evolution with plots of velocity as a function of stream position and height: partway through spin-up (top), just shy of turbulence, and after turbulence emerges. (Lighter hues correspond to larger velocities.) The researchers find that, when combined with an initial velocity profile that’s linear instead of logarithmic as commonly implemented, their approach can cut spin-up times by at least a factor of five. (K. S. Nelson, O. B. Fringer, Phys. Fluids 29, 105101, 2017 .)